Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
J Chem Phys. 2011 Dec 7;135(21):214101. doi: 10.1063/1.3663709.
Coarse-grained (CG) models enable highly efficient simulations of complex processes that cannot be effectively studied with more detailed models. CG models are often parameterized using either force- or structure-motivated approaches. The present work investigates parallels between these seemingly divergent approaches by examining the relative entropy and multiscale coarse-graining (MS-CG) methods. We demonstrate that both approaches can be expressed in terms of an information function that discriminates between the ensembles generated by atomistic and CG models. While it is well known that the relative entropy approach minimizes the average of this information function, the present work demonstrates that the MS-CG method minimizes the average of its gradient squared. We generalize previous results by establishing conditions for the uniqueness of structure-based potentials and identify similarities with corresponding conditions for the uniqueness of MS-CG potentials. We analyze the mapping entropy and extend the MS-CG and generalized-Yvon-Born-Green formalisms for more complex potentials. Finally, we present numerical calculations that highlight similarities and differences between structure- and force-based approaches. We demonstrate that both methods obtain identical results, not only for a complete basis set, but also for an incomplete harmonic basis set in Cartesian coordinates. However, the two methods differ when the incomplete basis set includes higher order polynomials of Cartesian coordinates or is expressed as functions of curvilinear coordinates.
粗粒化（CG）模型能够高效地模拟复杂过程，而这些过程无法通过更详细的模型进行有效研究。CG 模型通常使用力或结构驱动的方法进行参数化。本工作通过研究相对熵和多尺度粗粒化（MS-CG）方法，探讨了这些看似不同的方法之间的相似之处。我们证明，这两种方法都可以用一个信息函数来表示，该函数可以区分原子模型和 CG 模型生成的集合。虽然众所周知，相对熵方法最小化了这个信息函数的平均值，但本工作证明了 MS-CG 方法最小化了它的梯度平方的平均值。我们通过建立结构基势的唯一性条件，推广了以前的结果，并确定了与 MS-CG 势的唯一性相应条件的相似性。我们分析了映射熵，并扩展了 MS-CG 和广义 Yvon-Born-Green 形式用于更复杂的势。最后，我们提出了数值计算，突出了基于结构和力的方法之间的相似性和差异。我们证明了这两种方法不仅在完整基组中，而且在笛卡尔坐标系中的不完全谐波基组中都得到了相同的结果。然而，当不完全基组包括笛卡尔坐标的更高阶多项式或表示为曲线坐标的函数时，两种方法会有所不同。
